find the square root of complex number 2 + 2√3 i - Maths - Complex Numbers and Quadratic Equations

Question

find the square root of complex number 2 + 2√3 i

Rishabh Mittal · Accepted Answer

Dear Student,

Let x+iy=2+23iSquaring on both sides, we getx+iy2 = 2+23ix2+i2y2 +i2xy = 2+23ix2-y2 + i2xy = 2 +23iOn comparing both sides, we getx2-y2=2   
 i2xy = 23    
 iiWe know,x2+y22=x2-y22+4x2y2x2+y22=22 + 232x2+y22=4+12x2+y22=16x2+y2=4   
 iiiAdding i and iii2x2 = 6x2=3x=±3Substituting the value of x in ii, we get2±3y=23y=±1So, square root of 2+23i is ±3 ± i

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